Let A = {a, b, c}, B = {p, q, r} and `f: A rarr B` be given by
f = {(a, q), (b, r), (c, p)}. will `f^(-1)` exist ? justify your answer.

If f : R rarr R be given by f(x) = (3 - x^3)^(1/3) , then (f o f) (x) is

Let A = R - {-3} and B = R - {1} Consider the function f : A rarr B defined by f(x) = (x-2)/(x-3) . Is f one-one and onto ? Justify your answer.

Let A = R -{3} , B = R - {1} and let f: A rarr B be defined by f(x) = (x-2)/(x-3) . Check the nature of function.

Let f be the subset of Z xx Z defined by f = {(ab, a + b) : a,b in Z} is f a function from Z to Z? justify your answer.

If A xx B={(p, q),(p, r),(m, q),(m, r)} , fịnd A and B

Let R be a relation from N to N defined by R = {(a,b) in N and a = b^2} . Are the following true? (a,b) in R, (b,c) in R implies (a,c) in R . Justify your answer .

Let P={1,2,3} , Q={a, b} Find P x Q and Q x P

*: RxxRrarr R is given by a**b=3a^2-b .Find the value of 2*3.Is * commutative?Justify your answer.

Is it true that for any sets A and B , P (A) cup P (B) = P(A cup B) ? Justify your answer

Let A={-1,0,1,2,} B={-4,-2,0,2} and f, g: A rarr B be functions defined by f(x)=x^2-x, x in A and g(x)=2|x-1/2|-1, x in A .Are f and g equal?. Justify your answer.